Students at the University of Birmingham after their degree ceremony. Funding for teaching in English universities is to be cut for 2014-15. Photograph: Christopher Furlong/Getty Images

Universities have been forced to slash their teaching budgets in order to protect research funds in a move that the head of the university funding agency has admitted "will hurt".

University students will see their institution's teaching budgets slashed by nearly 6% after the Higher Education Funding Council for England (Hefce) revealed the details of its allocations for the 2014-15 academic year. A combination of lower funding from government and a requirement to protect research budgets means the cuts will come in the provision of teaching.

The National Union of Students (NUS)said the move would erode the quality of a university education.

Professor Madeleine Atkins, chief executive of Hefce, said: "Public funding is experiencing continuing constraints and the higher education sector is no exception. The cuts to teaching funding and the continued cash standstill in research funding will hurt universities. They come at a time of considerable change in higher education.

"The board has made some difficult decisions, balancing several competing interests. We are asking the sector to do more with fewer resources, but, with care, the reductions are manageable."

Hefce's announcement of the funding settlement also included an additional 30,000 undergraduates studying at universities in England from September 2014, in anticipation of the government's decision in the autumn statement to remove the cap on student numbers entirely from 2015.

The £3.88bn in total funding – part of the funding settlement previously announced by the Department for Business, Innovation and Skills (BIS) – will be divided up between 130 universities and higher education colleges and 212 further education colleges. While research funding was largely unchanged, the brunt of cuts will see teaching budgets shrinking by 5.9% in cash terms.

Hefce said that university teaching funding "is increasingly aimed at meeting the costs of teaching that cannot be covered by tuition fees alone", such as support for widening access and student retention, covering the expenses of high-cost subjects and helping small and specialist institutions. It said the cuts also reflected the continuing shift towards teaching being funded directly from tuition fees paid by students.

The NUS said the scale of the cuts were damaging for education. "The cuts to funding for teaching forced by the government are incredibly disappointing and further erode direct investment in learning," an NUS spokesperson said.

"The last thing we want to see is the government to continue to slash education funding in years to come. We need a future based on sustainable investment and that means a new deal for the next generation of students."

Pam Tatlow, the chief executive of million+, a thinktank backed by a group of new universities, said: "The background detail of the allocations is extremely complex, in part as the result of the mix of 'old regime' students still in the system, changes in student numbers and the attempts by Hefce to ensure that no one funding area takes more of a hit than others.

"However, there's no disguising the fact that overall funding for universities will decline in real terms by 2015."

The settlement by BIS followed the discovery of a black hole in its education funding budget – first revealed by the Guardian – owing to a blow-out in funding for students at private further education colleges. That led the department to apply unexpected cuts to the higher and further education sectors in order to balance its books.

The BIS settlement also required that Hefce protect "as far as possible" high-cost subjects, such as science, technology, engineering and maths, and additional funds for widening participation and access to higher education, funded through Hefce's student opportunity allocation.

When the funding totals were announced, the Russell Group of research universities warned that forced cuts in public funding for teaching "wouldn't be fair on those students and could have a detrimental impact on the quality of their education".

For postgraduates, around £130m will be allocated to support postgraduate study in 2014-15, with research supported by the £240m programme supervision fund – with both amounts unchanged from 2013-14.

Overall, Hefce has allocated £1.6bn in funding for research, £1.6bn for teaching, £440m for capital grants and £143m for national facilities and initiatives funding.

"Research funding is maintained in cash terms. Hefce will continue to fund research selectively, focusing on world-leading and internationally excellent activity. Support for universities undertaking research funded by charities or business and industry will also be maintained at current levels," Hefce said.